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One of the challenges in epidemiology is to account for the complexmorphological structure of hosts such as plant roots, crop fields, farms,cells, animal habitats and social networks, when the transmission of infectionoccurs between contiguous hosts. Morphological complexity brings an inherentheterogeneity in populations and affects the dynamics of pathogen spread insuch systems. We have analysed the influence of realistically complex hostmorphology on the threshold for invasion and epidemic outbreak in an SIR(susceptible-infected-recovered) epidemiological model. We show that disorderexpressed in the host morphology and anisotropy reduces the probability ofepidemic outbreak and thus makes the system more resistant to epidemicoutbreaks. We obtain general analytical estimates for minimally safe bounds foran invasion threshold and then illustrate their validity by considering anexample of host data for branching hosts (salamander retinal ganglion cells).Several spatial arrangements of hosts with different degrees of heterogeneityhave been considered in order to analyse separately the role of shapecomplexity and anisotropy in the host population. The estimates for invasionthreshold are linked to morphological characteristics of the hosts that can beused for determining the threshold for invasion in practical applications.

Complexity and anisotropy in host morphology make populations safer against epidemic outbreaks